Dynkin diagrams and crepant resolutions of quotient singularities

الأصل · EN

Let V be a complex vector space on which a finite group G acts by linear transformations. Let W = V ⊕ V* be the sum of V with its dual V*. We prove that if the quotient W/G admits a smooth crepant resolution, then the subgroup G ⊂ Aut V is generated by complex reflections. We also obtain some results on the structure of smooth crepant resolutions of the quotients W/G, where W is a symplectic vector space, and G ⊂ Aut W is a finite group of symplectic linear transformations of the vector space W.